Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Is it permissible for one who sacrifices on behalf of another, with the latter's permission, to eat from the sacrifice?
It is permissible for someone who sacrificed on behalf of another with their permission to eat from it with their permission, and they stand in their place (act as their representative) in distributing it.
It is stated in Nihayat al-Muhtaj ila Sharh al-Minhaj (Vol.8/P.141): "And he—meaning the one sacrificing on his own behalf, provided he has not apostatized—has the right to eat from a voluntary sacrifice and his sacrificial gift; rather, it is recommended. As for an obligatory sacrifice, it is forbidden for him to eat from it, whether it was designated as such initially or as a liability in his dhimmah. And excluded by what has preceded is if he sacrifices on behalf of another, or if he apostatized, then it is not permissible for him to eat from it, just as it is absolutely impermissible to feed a disbeliever from it."(The text I found indicates the impermissibility of eating) ???
And it is stated in Hashiyat al-Jamal ‘ala Sharh al-Manhaj (Vol.5/P.262): "If a person offers a sacrifice on behalf of a living person with their permission, does he act as their representative in distributing it—on the grounds that permission to sacrifice is permission to distribute it—or does it depend on their explicit permission? This requires consideration, but the first view is not far-fetched." And Allah the Almighty knows best.
Is it permissible to agree with a butcher to purchase the meat of an animal after it has been slaughtered — for instance, by buying the meat of a sheep at a price determined by the weight of its meat following slaughter, at a fixed rate per kilogram? And what is the ruling if the animal is being purchased with the intention of it being an uḍḥiyyah (sacrificial offering)?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible to sell livestock in the manner of pricing each kilogram of meat after slaughter at a fixed rate, because the meat within the animal prior to slaughter is unseen and unknown. This leads to jahālah (ignorance of the subject matter) and gharar (contractual uncertainty), both of which are among the invalidating factors in sales transactions.
However, it is permissible for the buyer to issue a promise to purchase the meat of the animal after slaughter at a specified price per kilogram, with the actual sale being concluded at the time of weighing the meat — at which point both the quantity of the goods and the total price become known. There is no Sharī'ah objection to this arrangement.
The jurists have stipulated that for a sale to be valid, both countervalues must be present and observable. Al-Khaṭīb al-Shirbīnī, may Allah have mercy upon him, states:
"It is valid to sell a heap of grain whose total measure is unknown to both contracting parties at a rate of one sā' per dirham. This sale is valid because the subject of sale is present and observable, and ignorance of the total price is not harmful since it is known in detail — and uncertainty is thereby lifted."— [Mughnī al-Muḥtāj, Vol.2/P.355]
As for the uḍḥiyyah, the 'aqīqah, and vowed blood sacrifices (al-dam al-mandhūr) — full ownership of the animal must be established prior to slaughter. It is not valid for such animals to be slaughtered while still in the ownership of the butcher. Rather, the animal must be purchased alive and then slaughtered with the intention of uḍḥiyyah or the like. And Allah Almighty knows best.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).